76 research outputs found
Multi-scale theory of rotating turbulence
We consider turbulence induced by an arbitrary forcing and derive turbulence
amplitude and turbulent transport coefficients, first by using a quasi-linear
theory and then by using a multi-scale renormalisation analysis. With an
isotropic forcing, the quasi-linear theory gives that the turbulent transport
coefficients, both parallel and perpendicular to the rotation vector, have the
asymptotic scaling for rapid rotation (i.e. when the rotation
rate is larger than the inverse of the correlation time of the forcing
and the diffusion time), while the renormalisation analysis suggests a weaker
dependence on , with scaling. The turbulence amplitude
is found to scale as in the rapid rotation limit
depending on the property of the forcing. In the case of an anisotropic
forcing, we find that non-diffusive fluxes of angular momentum scale as
for rapid rotation, depending on the temporal
correlation of the forcing
Magnetoconvection and dynamo coefficients: II. Field-direction dependent pumping of magnetic field
We study the pumping of magnetic flux in three-dimensional compressible
magnetoconvection in the context of stellar dynamos. The simulation domain
represents a rectangular section from the lower part of a stellar convection
zone plus the underlying stably stratified layer, with a total depth of up to
five pressure scale heights. Once convection has attained a statistically
stationary state, a magnetic field is introduced. The magnetic field is
subsequently modified by the convective motions, and the resulting pumping
effects are isolated by calculating various coefficients of the expansion of
the electromotive force, uxb, in terms of components of the mean magnetic
field. The dependence of the pumping effects on rotation, latitude and other
parameters is studied. First numerical evidence is found for the existence of
pumping effects in the horizontal directions, unless the rotation axis
coincides with the vertical axis, as is the case on the poles. Evidence is
found that the pumping effects act differently on different components of the
mean magnetic field. Latitudinal pumping is mainly equatorward for toroidal
field, and can be poleward for poloidal field. Longitudinal pumping is mainly
retrograde for the radial field but prograde for the latitudinal field. The
pumping effect in the vertical direction is found to be dominated by the
diamagnetic effect, equivalent to a predominating downward advection with a
maximum speed in the turbulent case of about 10 percent of the rms convective
velocity. Where possible, an attempt is made to identify the physical origin of
the effect. Finally, some consequences of the results for stellar dynamos are
discussed.Comment: 12 pages, 9 figures, submitted to A&A; version
Estimates of the Strouhal number from numerical models of convection
We determine the Strouhal number (hereafter St), which is essentially a
nondimensional measure of the correlation time, from numerical calculations of
convection. We use two independent methods to estimate St. Firstly, we apply
the minimal tau-approximation (MTA) on the equation of the time derivative of
the Reynolds stress. A relaxation time is obtained from which St can be
estimated by normalising with a typical turnover time. Secondly, we calculate
the correlation and turnover times separately, the former from the
autocorrelation of velocity and the latter by following test particles embedded
in the flow. We find that the Strouhal number is in general of the order of 0.1
to 1, i.e. rather large in comparison to the typical assumption in the
mean-field theories that St << 1. However, there is a clear decreasing trend as
function of the Rayleigh number and increasing rotation. Furthermore, for the
present range of parameters the decrease of St does not show signs of
saturation, indicating that in stellar convection zones, where the Rayleigh
numbers are much larger, the Strouhal number may indeed be significantly
smaller.Comment: 4 pages, 2 figures. To appear in a special volume of Astronomische
Nachrichten for the conference 'Dynamos of the Sun, Stars & Planets', held in
Freiburg, Oct 4th-6th, 200
Resonance enhanced turbulent transport
The effect of oscillatory shear flows on turbulent transport of passive scalar fields is studied by numerical computations based on the results provided by E. Kim [Physics of Plasmas 13, 022308 (2006)] . Turbulent diffusion is found to depend crucially on the competition between suppression due to shearing and enhancement due to resonances, depending on the characteristic time and length scales of shear flow and turbulence. Enhancements in transport occur for turbulence with finite memory time either due to Doppler or parametric resonances. Scalings of turbulence amplitude and transport are provided in different parameter spaces. The results suggest that oscillatory shear flows are not only less efficient in regulating turbulence, but also can enhance the value of turbulent diffusion, accelerating turbulent transport
Generation of coherent magnetic fields in sheared inhomogeneous turbulence: No need for rotation?
Coherent magnetic fields are often believed to be generated by the combination of stretching by differential rotation and turbulent amplification of magnetic field, via the so-called alpha effect. The latter is known to exist in helical turbulence, which is envisioned to arise due to both rotation and convection in solar-type stars. In this contribution, a turbulent flow driven by a nonhelical inhomogeneous forcing and its kinematic dynamo action are studied for a uniform magnetic field in the background of a linear shear flow. By using a quasilinear analysis and a nonperturbative method utilizing a time-dependent wave number, turbulence property and electromotive force are computed for arbitrary shear strength. Due to the large-scale shear flow, the turbulence is highly anisotropic, as a consequence, so is the electromotive force. The latter is found to exist even without rotation due to the combined effect of shear flow and inhomogeneous forcing, containing not only the alpha effect but also magnetic pumping (the gamma effect representing a transport of magnetic flux by turbulence). Specifically, without shear, only the magnetic pumping exists, aligned with the direction of inhomogeneity. For a weak but nonzero shear, the combined effects of shear and inhomogeneous forcing modify the structure of the magnetic pumping when the inhomogeneity is in the plane of the shear flow, the magnetic pumping becoming bidimensional in that plane. It also induces an alpha tensor which has nondiagonal components. When the inhomogeneity is perpendicular to the plane of the shear flow, the alpha effect has three nonzero diagonal components and one off-diagonal component. However, for a sufficiently strong shear, the gamma and alpha effects are suppressed due to shear stabilization which damps turbulence. A simplified dynamo model is then proposed where a large-scale dynamo arises due to the combined effect of shear flow and inhomogeneous forcing. In particular, the growth of a large-scale axisymmetric magnetic field is demonstrated in case of an inhomogeneity which is perpendicular to the plane of the shear flow. Interesting implications of these results for the structure of magnetic fields in star with slow rotation are discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3551700
Local models of stellar convection: Reynolds stresses and turbulent heat transport
We study stellar convection using a local three-dimensional MHD model, with
which we investigate the influence of rotation and large-scale magnetic fields
on the turbulent momentum and heat transport. The former is studied by
computing the Reynolds stresses, the latter by calculating the correlation of
velocity and temperature fluctuations, both as functions of rotation and
latitude. We find that the horisontal correlation, Q_(theta phi), capable of
generating horisontal differential rotation, is mostly negative in the southern
hemisphere for Coriolis numbers exceeding unity, corresponding to equatorward
flux of angular momentum in accordance with solar observations. The radial
component Q_(r phi) is negative for slow and intermediate rotation indicating
inward transport of angular momentum, while for rapid rotation, the transport
occurs outwards. Parametrisation in terms of the mean-field Lambda-effect shows
qualitative agreement with the turbulence model of Kichatinov & R\"udiger
(1993) for the horisontal part H \propto Q_(theta phi)/cos(theta), whereas for
the vertical part, V \propto Q_(r phi)/sin(theta), agreement only for
intermediate rotation exists. The Lambda-coefficients become suppressed in the
limit of rapid rotation, this rotational quenching being stronger for the V
component than for H. We find that the stresses are enhanced by the presence of
the magnetic field for field strengths up to and above the equipartition value,
without significant quenching. Concerning the turbulent heat transport, our
calculations show that the transport in the radial direction is most efficient
at the equatorial regions, obtains a minimum at midlatitudes, and shows a
slight increase towards the poles. The latitudinal heat transport does not show
a systematic trend as function of latitude or rotation.Comment: 26 pages, 20 figures, final published version. For a version with
higher resolution figures, see http://cc.oulu.fi/~pkapyla/publ.htm
Effect of rotation on the tachoclinic transport
We study the effect of rotation on sheared turbulence, due to differential
rotation. By solving quasi-linear equations for the fluctuating fields, we
derive turbulence amplitude and turbulent transport coefficients, taking into
account the effects of shear and rotation on turbulence. We focus on the
regions of the tachocline near the equator and the poles where the rotation and
the shear are perpendicular and parallel, respectively. For parameter values
typical of the tachocline, we show that the shear reduces both turbulence
amplitude and transport, more strongly in the radial direction than in the
horizontal one, resulting in an anisotropic turbulence. The rotation further
reduces turbulence amplitude and transport at the equator whereas it does not
have much effect near the pole. The interaction between the shear and the
rotation is shown to give rise to a novel non diffusive flux of angular
momentum, possibly offering a mechanism for the occurrence of a strong shear
region in the solar interior
The mean electro-motive force, current- and cross-helicity under the influence of rotation, magnetic field and shear
The mean electromotive force (MEMF) in a rotating stratified
magnetohydrodynamical turbulence is studied.Our study rests on the mean-field
magnetohydrodynamics framework and approximation. We compute the effects
of the large-scale magnetic fields (LSMF), global rotation and large-scale
shear flow on the different parts of the MEMF (such as - effect,
turbulent diffusion, turbulent transport, etc.) in an explicit form. The
influence of the helical magnetic fluctuations which stem from the small-scale
dynamo is taken into account, as well. In the paper, we derive the equation
governing the current helicity evolution. It is shown that the joint effect of
the differential rotation and magnetic fluctuations in the stratified media can
be responsible for the generation, maintenance and redistribution of the
current helicity. The implication of the obtained results to astrophysical
dynamos is considered as well.Comment: 27 pages, 8 figures, submitted to GAF
Differential rotation and meridional flow of Arcturus
The spectroscopic variability of Arcturus hints at cyclic activity cycle and
differential rotation. This could provide a test of current theoretical models
of solar and stellar dynamos. To examine the applicability of current models of
the flux transport dynamo to Arcturus, we compute a mean-field model for its
internal rotation, meridional flow, and convective heat transport in the
convective envelope. We then compare the conditions for dynamo action with
those on the Sun. We find solar-type surface rotation with about 1/10th of the
shear found on the solar surface. The rotation rate increases monotonically
with depth at all latitudes throughout the whole convection zone. In the lower
part of the convection zone the horizontal shear vanishes and there is a strong
radial gradient. The surface meridional flow has maximum speed of 110 m/s and
is directed towards the equator at high and towards the poles at low latitudes.
Turbulent magnetic diffusivity is of the order --. The conditions on Arcturus are not favorable for a
circulation-dominated dynamo
The alpha-effect in a turbulent liquid-metal plane Couette flow
We calculate the mean electromotive force in plane Couette flows of a
nonrotating conducting fluid under the influence of a large-scale magnetic
field for driven turbulence. A vertical stratification of the turbulence
intensity results in an alpha effect owing to the presence of horizontal shear.
Here we discuss the possibility of an experimental determination of the
components of the alpha tensor using both quasilinear theory and nonlinear
numerical simulations. For magnetic Prandtl numbers of the order of unity, we
find that in the high-conductivity limit the alpha effect in the direction of
the flow clearly exceeds the component in spanwise direction. In this limit,
alpha runs linearly with the magnetic Reynolds number Rm while in the
low-conductivity limit it runs with the product Rm*Re, where Re is the kinetic
Reynolds number so that for given Rm the alpha effect grows with decreasing
magnetic Prandtl number.
For the small magnetic Prandtl numbers of liquid metals, a common value for
the horizontal elements of the alpha tensor appears, which makes it unimportant
whether the alpha effect is measured in the spanwise or streamwise directions.
The resulting effect should lead to an observable voltage in both directions of
about 0.5 mV for magnetic fields of 1 kgauss and velocity fluctuations of about
1 m/s in a channel of 50 cm height (independent of its width).Comment: 9 pages, 6 figures, PRE, in pres
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